Nothing's going to be superior to lavaliere mics. The best microphone in the world will sound lousy if it's not placed correctly. If the camera is far away from the subject, don't expect great sound.
Physics. You can't deny it.
Booms and Lavs exist for good reason.
Since you're on a budget, I suggest getting a nice long pole, a smart PA to hold it, and putting the best 200 euro mic at the end of it.
Also, a decent (self) education on how to record audio and WHY sound does what it does ... it's such a good investment, don't overlook that part.